Transcript Semileptonic B Decays at BABAR

Semileptonic B Decays at BABAR
Masahiro Morii
Harvard University
BNL Particle Physics Seminar, 13 January 2005
Outline

Introduction



Measurements





13 January 2005
PEP-II and BABAR Experiment
Why semileptonic B decays?
Inclusive b → cℓv  |Vcb|, mb, mc
Inclusive b → uℓv  |Vub|
Exclusive B → D*ℓv  |Vcb|
Exclusive B → pℓv  |Vub|
Summary
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PEP-II Asymmetric B Factory

Collides 9 GeV e− against 3.1 GeV e+

ECM = 10.58 GeV = mass of U(4S)



Lightest bb resonance that decays into BB meson pair
Boost bg = 0.56 allows measurement of B decay times
Peak luminosity 9.2×1033/cm2/s  BB production ~10 Hz

More than 3× the design luminosity!
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3
PEP-II Luminosity
Run 4
Run 4

BABAR has accumulated 244 fb-1 of data

Run 4 (Sep’03-Jul’04) was a phenomenal success
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BABAR Detector
Photon energy with a
CsI(Tl) crystal
calorimeter
Charged particle
momentum with a drift
chamber in a 1.5 T field
Muons detected after
penetrating iron yoke
Particle ID with a
Cerenkov detector
(DIRC)
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Precise vertex with a
silicon strip detector
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B Mesons, CP violation

B Factories produce ~2×108 B mesons/year



B+ and B0 are the most accessible 3rd-generation particles
Their decays allow detailed studies of the CKM matrix

 Vud Vus Vub   d L 
g
L  uL cL tL  g   Vcd Vcs Vcb   sL W  h.c.
2
V V V  b 
ts
tb   L 
 td
Unitary matrix VCKM translates mass and weak basis

3 real parameters + 1 complex phase
The only source of CPV
in the Minimal SM
Is this the complete description of the CP violation?

Is everything consistent with a single unitary matrix?
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Unitarity Triangle


This is neatly represented by the familiar Unitarity Triangle

VudVub
VcdVcb
VtdVtb
VcdVcb
a
g
b


VudVub  VcdVcb  VtdVtb  0
†
VCKM
VCKM  1
Unitarity of VCKM
1
 VtdVtb* 
a  arg  * 
V
V
 ud ub 
 VcdVcb* 
b  arg  * 
V
V
 td tb 
 VudVub* 
g  arg  * 
V
V
 cd cb 
Angles a, b, g can be measured with CPV of B decays
Coming soon:
13 January 2005
Measurements of b from BABAR, by Soeren Prell, 1/20/05
Measurements of a and g from BABAR, by Malcolm John, 2/20/05
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Consistency Test

Compare the measurements (contours) on the (, ) plane


The
tells us this is true
as of today


If the SM is the whole story,
they must all overlap
Still large enough for New
Physics to hide
Precision of sin2b outstripped
the other measurements

Must improve the others to
make more stringent test
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Next Step: |Vub/Vcb|

Zoom in to see the overlap of “the other” contours


It’s obvious: we must make
the green ring thinner
Left side of the Triangle is
VudVub Vub 1


VcdVcb Vcb tan C
Measurement of |Vub/Vcb| is
complementary to sin2b
Goal: Accurate determination of both |Vub/Vcb| and sin2b
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Semileptonic B Decays

Semileptonic decays offer a clear view of the b quark in the B
mesons

-
decoupled from
hadronic effects
W
b
Vcb ,Vub

c, u
Analogous to deep-inelastic scattering

b
-
W
c, u

Good probe for |Vcb| and |Vub|
 We can also study the structure of the
B meson
X c ,u
B
More on this
as we go
u, d
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Experimental Approaches

Inclusive: B → Xcℓv or Xuℓv
Tree-level rates are
GF2
2
5
B
Gu  G(b  u  ) 
V
m
ub
b
192p 2
GF2
2
2
3
Gc  G(b  c  ) 
V
m
(
m
m
)
cb
b
b
c
192p 2



QCD corrections must be calculated


Operator Product Expansion (OPE)
How do we separate Xu from Xc?


X
Focus of this talk
Gc = 50 × Gu  Much harder problem for |Vub|
Exclusive: B → D*ℓv, Dℓv, pℓv, ℓv, etc.

Need form factors to relate the rate to |Vcb|, |Vub|
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Inclusive |Vcb|

Operator Product Expansion allows calculation of

Inclusive rate
 Lepton energy (Eℓ) moments
 Hadron mass (mX) moments


B
Expansion in terms of 1/mb and as(mb)
Separate short- and long-distance effects at  ~ 1 GeV
 Perturbative corrections calculable from mb, mc, as(mb)



Xc
Non-perturbative corrections cannot be calculated
3
 Ex: 4 parameters up to O (1/ mb ) in the kinetic scheme
Strategy: Measure rate + as many moments as possible

Determine all parameters by a global fit
 Over-constrain to validate the method
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Observables

Define 8 moments from inclusive Eℓ and mX spectra
M0
M1
dG


Partial branching fraction
GB
E dG


 dG
M iX 

i
m
 X dG
 dG
Mi
E



- M1  d G
i
 dG
(i  1, 2,3, 4)
(i  2,3)
Lepton energy
moments
Hadron mass
moments
Integrations are done for Eℓ > Ecut, with Ecut varied in 0.6–1.5 GeV
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BABAR PR D69:111104
Electron Energy Moments


BABAR data, 47.4 fb-1 on U(4S) resonance + 9.1 fb-1 off-peak
Select events with 2 electrons
Unlike-sign
BABAR



One (1.4 < p* < 2.3 GeV) to
“tag” a BB event
The other (p* > 0.5 GeV) to
measure the spectrum
Use charge correlation

Unlike-sign events


Like-sign
dominated by B  Xcev
Like-sign events

D  Xev decays, B0 mixing
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BABAR PR D69:111104
Electron Energy Moments

Turn the like-/unlike-sign
spectra  Eℓ spectrum




BABAR
Divide by the efficiency
Account for B0 mixing
Correct for the detector
material (Bremsstrahlung)
Calculate the moments for Ecut = 0.6 … 1.5 GeV



Move from U(4S) to B rest frame
Correct for the final state radiation using PHOTOS
Subtract B  Xuℓv
Into the OPE fit
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BABAR PR D69:111103
Hadron Mass Moments


BABAR data, 81 fb-1 on U(4S) resonance
Select events with a fully-reconstructed B meson


Use ~1000 hadronic decay chains
Rest of the event contains one “recoil” B




Flavor and momentum known
Find a lepton with E > Ecut in the recoil-B

v
Lepton charge consistent with the B flavor
mmiss consistent with a neutrino
lepton
All left-over particles belong to Xc

Fully reconstructed
B  hadrons
Improve mX with a kinematic fit  s = 350 MeV

Xc
4-momentum conservation; equal mB on both sides; mmiss = 0
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BABAR PR D69:111103
Hadron Mass Moments

Measured mX < true mX

Linear relationship
 Calibrate using simulation


Depends (weakly) on decay
2
multiplicity and mmiss
Validate calibration procedure



BABAR
Simulated events in exclusive
final states
D*±  D0p ± in real data, tagged
by the soft p ±
Calculate mass moments with Ecut = 0.9 … 1.6 GeV
Into the OPE fit
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BABAR PRL 93:011803
Inputs to OPE Fit
Error bars are stat. & syst.
with comparable sizes
mX moments
BABAR
Eℓ moments
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BABAR PRL 93:011803
Fit Parameters

Calculation by Gambino & Uraltsev (hep-ph/0401063 & 0403166)




Kinetic mass scheme to O (1/ mb3 )
Eℓ moments O (a s2 )
mX moments O (a s )
8 parameters to determine
Vcb

kinetic
chromomagnetic
3
mb mc B ( B  X c  ) p2 G2  D3  LS
8 moments available with several Ecut


O (1/ mb2 )
Sufficient degrees of freedom to determine
all parameters without external inputs
Fit quality tells us how well OPE works
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spin-orbit
Darwin
O (1/ mb3 )
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BABAR PRL 93:011803
Fit Results
● = used, ○ = unused
in the nominal fit
mX moments
BABAR
c 2/ndf = 20/15
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Red line: OPE fit
Yellow band: theory errors
Eℓ moments
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BABAR PRL 93:011803
Fit Consistency

OPE describes BABAR data very well
 c 2/ndf = 20/15

Separate fit of Eℓ and mX moments agree
BABAR
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BABAR PRL 93:011803
Fit Results
Vcb  (41.4  0.4exp  0.4HQE  0.6 th ) 10 -3
Bc   (10.61  0.16exp  0.06HQE )%
Uncalculated
corrections to G
mb  (4.61  0.05exp  0.04HQE  0.02as ) GeV
mc  (1.18  0.07 exp  0.06HQE  0.02as ) GeV
p2  (0.45  0.04exp  0.04HQE  0.01a ) GeV 2
s
  (0.27  0.06exp  0.03HQE  0.02a ) GeV
2
G
2
s
kinetic mass scheme
with  = 1 GeV
 D3  (0.20  0.02exp  0.02HQE  0.00a ) GeV 3
s
3
 LS
 (-0.09  0.04exp  0.07 HQE  0.01a ) GeV 3
s



3
p2 and  LS
consistent with B-B* mass splitting and QCD sum rules
p2  G2 and the scale of  D3 consistent with theoretical expectations
Remarkable agreement between data and theory
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Heavy Quark Masses

Convert mb and mc into MS scheme (N. Uraltsev)
mbkin (1GeV)  (4.61  0.05exp  0.04HQE  0.02th )GeV
mb (mb )  4.22  0.06GeV
mckin (1GeV)  (1.18  0.07exp  0.06HQE  0.02th )GeV
mc (mc )  1.33  0.10GeV
theory
theory
References in PDG 2002
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Inclusive |Vcb| in Perspective

BABAR result compares well with previous measurements

|Vcb| is now measured to ±2%
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Inclusive |Vub|
GF2
2
5
V
m
 |Vub| can be measured from Gu  G(b  u  ) 
ub
b
192p 2

The problem: b → cℓv decay
2
G(b  u  ) Vub
1


2
G(b  c  ) Vcb
50

How can we suppress
50× larger background?
Use mu << mc  difference in kinematics



Maximum lepton energy 2.64 vs. 2.31 GeV
First observations (CLEO, ARGUS, 1990)
used this technique
Only 6% of signal accessible

How accurately do we know this fraction?
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bc
b u
E
25
b → uℓv Kinematics

There are 3 independent variables in B → Xℓv

Take Eℓ, q2 (lepton-neutrino mass2), and mX (hadronic mass)
q 2
E
6%
mX
20%
70%
Technique
Efficiency
Theoretical Error
Eℓ
Straightforward
Low
Large
q2
Complicated
Moderate
Moderate
mX
Complicated
High
Large
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Where does it
come from?
26
Theoretical Issues


-
Tree level rate must be corrected for QCD
Operator Product Expansion gives us
the inclusive rate
B
 Expansion in as(mb) (perturbative)

and 1/mb (non-perturbative)
2
GF2 Vub mb5 
 as
G( B  X u  ) 
1
O


192p 3 
p
 92 - 1

2
2mb

known to O(as2)





Xu
Suppressed by 1/mb2
Main uncertainty (±10%) from mb5  ±5% on |Vub|
But we need the accessible fraction (e.g., Eℓ > 2.3 GeV) of the rate
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Shape Function

OPE doesn’t work everywhere in the phase space



OK once integrated
Doesn’t converge, e.g., near the Eℓ end point
Resumming turns non-perturb. terms into a Shape Function


≈ b quark Fermi motion parallel to the u quark velocity
Smears the quark-level distribution  observed spectra
Rough features (mean,
r.m.s.) are known
Details, especially the
tail, are unknown
f (k )
0
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  M B - mb
k
28
Shape Function – What to Do?

Measure: Same SF affects (to the first order) b → sg decays
Measure Eg
spectrum in
b → sg

Extract f(k+)
Predict Eℓ
spectrum in
b → uℓv
Caveat: whole Eg spectrum is needed

Only Eg > 1.8 GeV has been measured
 Background overwhelms lower energies

1.8
Eg
Compromise: assume functional forms of f(k+)
a (1 a ) x
; x
 Example: f ( k )  N (1 - x) e
k

2 parameters
( and a) to fit
Fit b → sg spectrum to determine the parameters
 Try different functions to assess the systematics

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CLEO hep-ex/0402009
SF from b → sg

Belle hep-ex/0407052
CLEO and Belle has measured the b → sg spectrum

BABAR result on the way
Belle
Eg
3 models tried
Fit
f (k )

I use the SF from the Belle data for the rest of the talk
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Measurements

BABAR has measured |Vub| using four different approaches
Technique
Eℓ > 2.0 GeV
Eℓ vs. q2
mX < 1.55 GeV
mX vs. q2


Reference
hep-ex/0408075
hep-ex/0408045
hep-ex/0408068
Inclusive B → Xev sample.
High statistics, low purity.
Recoil of fully-reconstructed B.
High purity, moderate statistics.
Statistical correlations are small
Different systematics, different theoretical errors
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BABAR hep-ex/0408075
Lepton Endpoint


BABAR data, 80 fb-1 on U(4S) resonance
Select electrons in 2.0 < Eℓ < 2.6 GeV


Push below the charm threshold
 Larger signal acceptance
 Smaller theoretical error
Accurate subtraction of background
is crucial!


Data (continuum sub)
MC for BB background
Data (eff. corrected)
MC
Data taken below the U4S resonance
for light-flavor background
Fit the Eℓ spectrum with b → uℓv,
B → Dℓv, B → D*ℓv, B → D**ℓv,
etc. to measure B(B  X u e , Ee  2.0GeV)  (4.85  0.29stat  0.53sys ) 10-4
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BABAR hep-ex/0408075
Lepton Endpoint

CLEO PRL 88:231803
BELLE-CONF-0325
Translate B into |Vub|

Compare results with different Eℓ cut
Eℓ (GeV)
B (10-4)
|Vub| (10-3)
BABAR
2.0–2.6
4.85 ± 0.29stat ± 0.53sys 4.40 ± 0.13stat ± 0.25sys ± 0.38theo
CLEO
2.2–2.6
2.30 ± 0.15exp ± 0.35sys 4.69 ± 0.15stat ± 0.40sys ± 0.52theo
Belle
2.3–2.6
1.19 ± 0.11exp ± 0.10sys 4.46 ± 0.20stat ± 0.22sys ± 0.59theo

Theoretical error reduced with lower Eℓ cut
13 January 2005
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BABAR hep-ex/0408045
Eℓ vs.

2
q
Use pv = pmiss in addition to pe  Calculate q2

Given Ee and q2, maximum hadronic mass squared is
max
h
s
 m 2  q 2 - 2 m E 1 b - 2m
 B
B e 1 b
B

2
2
2

m

q
2
m
q
B
B

max
 sh
q2
4 Ee
1 b
1 b
if  Ee  
q 2 1 b
2 1 b
b = B boost in
the c.m.s.
otherwise
 mD2 gives optimum separation of B → Xuev from Xcev
Xcev background
13 January 2005
Xuev signal
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BABAR hep-ex/0408045
Eℓ vs.

BABAR data, 80 fb-1 on resonance




2
q
Subtract off-peak data
Subtract BB background
normalized by sideband
Signal efficiency corrected by
B → D(*)ev control samples
Inclusive BF measured to be
-3
B  (2.76  0.26stat  0.50syst -0.21
)

10
0.26SF

Translate to |Vub|
-3
Vub  (4.99  0.48exp -0.18

0.22
)

10
OPE
0.23SF
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BABAR hep-ex/0408068
Measuring mX and

Same recoil technique as the b → cℓv mX moment measurement




Find a lepton (pℓ > 1GeV) in recoil B
Lepton charge consistent with the B flavor
mmiss consistent with a neutrino
Fully reconstructed
B  hadrons
All left-over particles belong to X



2
q
Improve mX with a kinematic fit
Calculate q2 of lepton-neutrino
Sample is mostly b → cℓv at this stage

Need some charm rejection cuts
13 January 2005
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v
lepton
X
36
BABAR hep-ex/0408068
Charm Suppression

Suppress b → cℓv by vetoing against D(*) decays


D decays usually produce at least one kaon
 Reject events with K± and KS
B0 → D*+(→ D0p +)ℓ−v has peculiar kinematics
 p + almost at rest w.r.t. D*+
 D*+ momentum can be estimated from p + alone
2
2
 Calculate m  ( pB - p - p ) for all p +
D
 Reject events consistent with mv = 0
*

Vetoed events are depleted in b → uℓv


Use them to validate simulation of background distributions
We’ve got (mX, q2) distribution of a signal-enriched sample
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BABAR hep-ex/0408068
Fitting mX

BABAR data, 80 fb-1 on resonance

BABAR

Simple fit in mX shows clear b → uℓv
signal
Inclusive BF measured to be
-3
B ( B  X u l )  (2.81  0.32stat  0.31sys -0.23
)

10
0.21theo
BABAR
13 January 2005
Vub  (5.22  0.30stat  0.31syst  0.43theo ) 10-3
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BABAR hep-ex/0408068
Fitting mX vs.

2
q
2-D fit to measure B in {mX < 1.7, q2 > 8}

Good resolution allows clean
extraction of B
-3
B  (0.90  0.14stat  0.14syst -0.01
)

10
theo
0.02

Signal event fraction into the “box”
calculated by Bauer et al.

Vub
hep-ph/0111387
192p 3 B

 BGF2 mb5 G
G = 0.282 ± 0.053
 (4.98  0.40stat  0.39syst  0.47 theo ) 10-3
13 January 2005
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39
BABAR hep-ex/0408075
Inclusive |Vub| Results

BABAR hep-ex/0408045
BABAR hep-ex/0408068
Summary of BABAR |Vub| results
Technique
|Vub| × 103
(SF) × 103
Eℓ > 2.0 GeV
4.40 ± 0.13stat ± 0.25sys ± 0.38theo
0.46
Eℓ vs. q2
4.99 ± 0.23stat ± 0.42sys ± 0.32theo
0.42
mX < 1.55 GeV
5.22 ± 0.30stat ± 0.31sys ± 0.43theo
0.45
mX vs. q2
4.98 ± 0.40stat ± 0.39sys ± 0.47theo
0.06


Statistical correlation between the mX and
mX-q2 results is 72%. Others negligible
Theoretical error of the mX-q2 result is
different from the rest  Negligible SF
dependence
13 January 2005
M. Morii, Harvard
How much |Vub|
moves if the SF
is determined by
the CLEO data
40
Inclusive |Vub| in Perspective
Eℓ endpoint
mX fit
mX vs. q2
Eℓ vs. q2
Results have been re-adjusted by
the Heavy Flavor Averaging Group

|Vub| is measured to ±9%?
13 January 2005
M. Morii, Harvard
41
Caveats + Outlook

Improved precision of |Vub| require re-evaluation of theoretical
uncertainties

Poor convergence of OPE calculation in the small mX region


NLO(1/mb) non-perturbative corrections differ between b → uℓv
and b → sg


Quantitative estimates in literature more-or-less agree
Weak annihilation diagrams may have large (20%?) effect near
the lepton energy endpoint


Improved calculations using SCET available now
Difference between B0 and B+ needs to be measured
Theory and experiment join forces to push the limit
13 January 2005
M. Morii, Harvard
42
Exclusive |Vcb|

B  D*ℓv decay rate is given by
form factor
2
d G( B  D l ) G Vcb
2
d

F
(
w
)
G( w)
3
dw
48p
*
2
F
phase space
D* boost g in the B rest frame


F(w) is calculable at w = 1, i.e. zero-recoil

F(1) = 1 at the heavy-quark limit (mb = mc = ∞)

Lattice calculation gives F (1)  0.919-0.030
0.035 Hashimoto et al,
PRD 66 (2002) 014503
Shape of F(w) unknown
 Parameterized with 2 (slope at w = 1) and R1, R2


Use R1 and R2 determined by CLEO, PRL 76 (1996) 3898
Measure dG/dw to fit F(1)|Vcb| and 2
13 January 2005
M. Morii, Harvard
43
BABAR hep-ex/0408027
B  D*ℓv Sample



BABAR data, 80 fb-1 on U(4S)
Find events with D*+ + lepton

D*  D 0p  with
D0  K -p  , K -p p -p  , K -p p 0

1.2 < pℓ < 2.4 GeV/c
Background

Fake D*


D* – D mass difference
True D* but not B  D*ℓv
cos  BY
13 January 2005
2 EB ED* - mB2 - mD2 *

2 pB pD*
M. Morii, Harvard
44
BABAR hep-ex/0408027
Determination of F(1)|Vcb|

Correct for efficiency  w distribution


Slow pion (from D* decays)
efficiency depend on w
Fitting dN/dw, we find
F (1) Vcb  (34.03  0.24stat  1.31syst ) 10-3
 2  1.23  0.02stat  0.28syst
BD*   (4.68  0.03stat  0.29syst )%
13 January 2005
M. Morii, Harvard
45
Determination of |Vcb|

BABAR result compares well
with existing measurements
 Results have been adjusted
to use common inputs

Using F(1) = 0.91 ± 0.04,
the world average is
Vcb  (41.4  1.0expt  1.8theo ) 10-3


13 January 2005
M. Morii, Harvard
Agrees with the inclusive
measurement
Accuracy ±5%
46
Exclusive |Vub|

Measure specific final states, e.g., B → pℓv




Good signal-to-background ratio
Branching fraction in O(10-4)  Statistics limited
So far B → pℓv and ℓv have been measured
 Also seen: B(B → wℓv) = (1.3±0.5)×10−4 [Belle hep-ex/0402023]
B(B → ℓv) = (0.84±0.36)×10−4 [CLEO PRD68:072003]
Need Form Factors to extract |Vub|
GF2
d G( B  p  )
2
3
2 2
 e.g.

Vub pp f  (q )
2
3
dq
24p

How are they calculated?
13 January 2005
M. Morii, Harvard
47
Form Factors

Form Factors are calculated using:

Lattice QCD (q2 > 16 GeV2)


Light Cone Sum Rules (q2 < 16 GeV2)


Assumes local quark-hadron duality  ~10% uncertainty
All of them have uncontrolled uncertainties


Existing calculations are “quenched”  ~15% uncertainty
LQCD and LCSR valid in different q2 ranges  No crosscheck
Unquenched LQCD starts to appear


Preliminary B → pℓv FF from FNAL+MILC (hep-lat/0409116),
HPQCD (hep-lat/0408019)
Current technique cannot do B → ℓv
13 January 2005
M. Morii, Harvard
48
Measurements

Concentrate on B → pℓv
B Sample
B(B → pℓv) × 104
q2 bins Reference
Recoil of B → hadrons
1.08 ± 0.28stat ± 0.16sys
1
hep-ex/0408068
Recoil of B → D*ℓv
1.46 ± 0.27stat ± 0.35sys
3
[ICHEP 2004]
Belle
Recoil of B → D(*)ℓv
1.76 ± 0.28stat ± 0.20sys
3
hep-ex/0408145
CLEO
Untagged
1.33 ± 0.18stat ± 0.13sys
3
PR D68,072003
BABAR


Total rate is measured to ~12% accuracy
Need measurement in bins of q2
LQCD calculation of FF available above 16 GeV2
 Small rate  Large statistical errors


New measurements + unquenched LQCD calculations will
make |Vub| extraction possible
13 January 2005
M. Morii, Harvard
49
Summary

Semileptonic decays provide excellent probes for the weak and
strong physics of the B mesons
 |Vcb| and |Vub|  Complementary to sin2b from CP violation


Heavy quark masses and the non-perturbative parameters
|Vcb| has been determined to ±2%

OPE fit of Eℓ and mX moments by BABAR gives
Vcb  (41.4  0.4exp  0.4HQE  0.6th ) 10-3


Fit quality and consistency support validity of the OPE application
Exclusive B  D*ℓv measurements agree
Vcb  (41.4  1.0expt  1.8theo ) 10-3 World average by HFAG
13 January 2005
M. Morii, Harvard
50
Summary

Significant progress in determination of |Vub|

Four (!) BABAR measurements of |Vub| with inclusive b → uℓv
Technique
|Vub| × 103
Eℓ > 2.0 GeV
4.40 ± 0.13stat ± 0.25sys ± 0.38theo
Eℓ vs. q2
4.99 ± 0.23stat ± 0.42sys ± 0.32theo
mX < 1.55 GeV
5.22 ± 0.30stat ± 0.31sys ± 0.43theo
mX vs. q2
4.98 ± 0.40stat ± 0.39sys ± 0.47theo


Overall accuracy of |Vub| around 10%
New measurements of B → pℓv + unquenched LQCD
calculations will measure |Vub| soon
13 January 2005
M. Morii, Harvard
51